Measurement of $CP$ asymmetry in $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays

A measurement of the $CP$-violating parameters in $B_s^0\to D_s^{\mp }{K}^{\pm }$ decays is reported, based on the analysis of proton-proton collision data collected by the LHCb experiment corresponding to an integrated luminosity of $6{\mathrm{f}\mathrm{b}}^{-1}$ at a centre-of-mass energy of $13\mathrm{T}\mathrm{e}\mathrm{V}$. The measured parameters are obtained with a decay-time dependent analysis yielding $C_f=0.791\pm 0.061\pm 0.022$, $A_f^{\mathrm{\Delta }\mathrm{\Gamma }}=-0.051\pm 0.134\pm 0.058$, $A_{\bar{f}}^{\mathrm{\Delta }\mathrm{\Gamma }}=-0.303\pm 0.125\pm 0.055$, $S_f=-0.571\pm 0.084\pm 0.023$ and $S_{\bar{f}}=-0.503\pm 0.084\pm 0.025$, where the first uncertainty is statistical and the second systematic. This corresponds to $CP$ violation in the interference between mixing and decay of about $8.6\sigma$. Together with the value of the Bs mixing phase $-2{\beta }_s$, these parameters are used to obtain a measurement of the CKM angle $\gamma$ equal to $(74\pm 12{)}^{\circ }$ modulo ${180}^{\circ }$, where the uncertainty contains both statistical and systematic contributions. This result is combined with the previous LHCb measurement in this channel using $3{\mathrm{f}\mathrm{b}}^{-1}$ resulting in a determination of $\gamma =(81_{-11}^{+12}{)}^{\circ }$.